Discount: Formula, Percentage, Tricks and Questions

Discount is the reduction given on the marked price of an article. This topic covers discount percentage, marked price, selling price, successive discounts and reverse calculations. The formulas also explain how discount combines with profit or loss in quantitative aptitude questions.

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What Is Discount?

Discount is the amount reduced from the marked price of an article. It is calculated as the difference between the marked price and the selling price.

If the marked price is MP and the selling price is SP, then Discount = MP − SP. Discount percentage is calculated on the marked price: Discount% = (Discount ÷ MP) × 100. Therefore, SP = MP × (100 − Discount%) ÷ 100. For example, if MP = ₹800 and the discount is 15%, the discount is ₹120 and SP is ₹680.

Discount Formula & Tricks

Important Formulas

Discount Amount
Discount = Marked Price − Selling Price

The discount amount is the difference between the marked price and the actual selling price.

Discount Percentage
Discount% = (Discount ÷ Marked Price) × 100

Discount percentage is always calculated with the marked price as the base.

Selling Price After Discount
SP = MP × (100 − d) ÷ 100

Here, MP is the marked price and d is the discount percentage.

Marked Price
MP = SP × 100 ÷ (100 − d)

This formula finds the marked price when the selling price and discount percentage are known.

Successive Discounts
Equivalent discount = a + b − (ab ÷ 100)

For discounts of a% and b% applied successively, the equivalent single discount is a + b − ab/100.

Discount with Profit
SP = CP × (100 + Profit%) ÷ 100 = MP × (100 − Discount%) ÷ 100

Equating both expressions for SP connects cost price, profit percentage, marked price and discount.

Quick Tricks

Use the Remaining Percentage

After a discount of d%, the customer pays (100 − d)% of the marked price. This avoids calculating the discount amount separately.

Example: For a 25% discount on ₹1,200, SP = 75% of ₹1,200 = ₹900.
Convert Successive Discounts Directly

For two successive discounts, subtract the product of the percentages divided by 100 from their sum.

Example: 20% and 10% successive discounts give 20 + 10 − (20 × 10)/100 = 28%, not 30%.
Find the Required Marked Price from SP

Divide the selling price by the fraction paid after discount. For a d% discount, divide SP by (100 − d)/100.

Example: If SP is ₹720 after a 10% discount, MP = ₹720 ÷ 0.90 = ₹800.

Discount Concepts

Marked Price, Selling Price and Discount

Marked price is the labelled price, selling price is the price paid after reduction, and discount is their difference.

The basic relation is MP = SP + Discount. If an article marked at ₹1,500 is sold for ₹1,275, the discount is ₹225. Its discount percentage is (225 ÷ 1,500) × 100 = 15%.

Example: MP = ₹2,000 and discount = ₹300. Therefore, SP = ₹2,000 − ₹300 = ₹1,700, and discount percentage = 15%.

Discount Percentage and Selling Price

The selling price after a discount of d% is (100 − d)% of the marked price.

Use SP = MP × (100 − d)/100. The discount percentage is based on MP, not SP. For a marked price of ₹2,400 and a discount of 12.5%, SP = ₹2,400 × 87.5/100 = ₹2,100.

Example: A 30% discount on ₹900 leaves 70% payable: SP = ₹900 × 70/100 = ₹630.

Successive Discounts

Successive discounts are applied one after another, so the second discount is calculated on the reduced price.

For discounts a% and b%, equivalent discount = a + b − ab/100. For 25% followed by 20%, the equivalent discount is 25 + 20 − (25 × 20)/100 = 40%. The final price is 60% of MP.

Example: If MP = ₹1,000, after 25% discount the price is ₹750; after another 20%, it is ₹600. Total reduction is ₹400, or 40%.

Discount and Profit or Loss

When an article is sold after discount, its selling price can also be expressed using cost price and profit or loss percentage.

For a profit of p%, SP = CP × (100 + p)/100. For a loss of l%, SP = CP × (100 − l)/100. Equating this with MP × (100 − d)/100 gives relations between MP, CP and the discount.

Example: If CP = ₹800, profit = 20% and discount = 4%, then SP = ₹960. Hence MP = ₹960 × 100/96 = ₹1,000.

Reverse Calculation of Marked Price

When the selling price and discount percentage are given, divide the selling price by the percentage retained to find the marked price.

Use MP = SP × 100/(100 − d). If the discount is 16%, the retained percentage is 84%. Thus, for SP = ₹1,050, MP = ₹1,050 × 100/84 = ₹1,250.

Example: An article sold for ₹1,440 after a 20% discount has MP = ₹1,440 × 100/80 = ₹1,800.

Discount Video Lessons

Watch short topic-wise lessons for quick revision.

6 Lessons
Lesson 1 of 6 Quick Revision

Successive Discounts and Equivalent Discount

Learn how to calculate the effective discount resulting from successive discounts and convert multiple discounts into an equivalent single discount using standard formulas.

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Practice Discount Questions

Practise published questions related to this topic.

1After allowing a discount of 11% on the marked price of an article, it is sold for ₹41,207. Find its marked price (in ₹).→ 2After successive discounts of 15% and 10%, a customer pays ₹3,672. What was the marked price?→ 3The difference between cost price and selling price of an article is Rs. 504. Loss percentage is 18 percent. What is the selling price of the article?→ 4By selling an article for Rs. 85000, a man incurs a loss of 15%. What should be the selling price to gain 15%?→ 5An agent sells a pressure cooker with a marked price of ₹8,460 at a discount of 30%. What is the selling price (in ₹) of the pressure cooker?→ 6A shopkeeper buys a watch for ₹400 and sells it at a profit of 12.5%. What is the selling price?→ 7An article is marked 25% above its cost price. A discount is offered so that a profit of 15% is made. Find the discount percentage.→ 8If the selling price of a bed is 6 times the initial selling price, the profit is 8 times the initial profit. Find the initial profit percentage (in %).→ 9The marked price of a toy truck is ₹8,810, and its selling price is ₹6,250. Find the discount percentage. (Round off the answer to two decimal places.)→ 10During a sale, 44% of the goods are sold at a 28% profit, 25% of the remaining goods are sold at a 48% profit and the rest are sold at an 18% loss. If there is an overall profit of x%, then what is the value of x?→

Discount Quick Quiz

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Quick Revision Notes

Discount Revision Points

Recall these relations for quick calculation of discount questions.

  • Discount = MP − SP.
  • Discount% = (Discount ÷ MP) × 100.
  • SP = MP × (100 − discount%) ÷ 100.
  • MP = SP × 100 ÷ (100 − discount%).
  • After a d% discount, the buyer pays (100 − d)% of MP.
  • Two successive discounts a% and b% are equivalent to a + b − ab/100.
  • Discount percentage is calculated on marked price, not selling price.
  • For profit, SP = CP × (100 + profit%) ÷ 100; for loss, SP = CP × (100 − loss%) ÷ 100.

Discount FAQs

What is the formula for discount percentage?

Discount% = (Discount ÷ Marked Price) × 100, where Discount = Marked Price − Selling Price.

What is the selling price after a 15% discount on ₹2,000?

The buyer pays 85% of ₹2,000. Therefore, SP = ₹2,000 × 85/100 = ₹1,700.

How are two successive discounts of 10% and 20% calculated?

Equivalent discount = 10 + 20 − (10 × 20)/100 = 28%. The final price is 72% of the marked price.

What is the marked price if the selling price is ₹1,275 after a 15% discount?

MP = ₹1,275 × 100/85 = ₹1,500.

Is a 20% discount followed by a 10% discount equal to a 30% discount?

No. The equivalent discount is 20 + 10 − (20 × 10)/100 = 28%, because the second discount applies to the reduced price.

An article costs ₹800 and is sold at a 20% profit after a 4% discount. What is its marked price?

SP = ₹800 × 120/100 = ₹960. Since SP is 96% of MP, MP = ₹960 × 100/96 = ₹1,000.

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